Decomposable pseudodistances and applications in statistical estimation |
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Authors: | Michel Broniatowski Aida Toma Igor Vajda |
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Institution: | 1. Laboratoire de Statistique Théorique et Appliquée, Université Paris 6, 4 Place Jussieu, 75005 Paris, France;2. Department of Applied Mathematics, Bucharest Academy of Economic Studies, Pia?a Roman? 6, Bucharest, Romania;3. “Gheorghe Mihoc – Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics, Calea 13 Septembrie 13, Bucharest, Romania;4. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod Vodarenskou, Vezi 4, 18208 Prague, Czech Republic |
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Abstract: | The aim of this paper is to introduce new statistical criteria for estimation, suitable for inference in models with common continuous support. This proposal is in the direct line of a renewed interest for divergence based inference tools imbedding the most classical ones, such as maximum likelihood, Chi-square or Kullback–Leibler. General pseudodistances with decomposable structure are considered, they allowing defining minimum pseudodistance estimators, without using nonparametric density estimators. A special class of pseudodistances indexed by α>0, leading for α↓0 to the Kullback–Leibler divergence, is presented in detail. Corresponding estimation criteria are developed and asymptotic properties are studied. The estimation method is then extended to regression models. Finally, some examples based on Monte Carlo simulations are discussed. |
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Keywords: | Divergence Pseudodistance Influence function Robustness Parametric model Regression |
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